The hamstrings to quadriceps functional ratio expressed over the full angle-angular velocity range using a limited number of data points

The hamstring to quadriceps (H : Q) strength ratio is widely used to identify individuals at risk of sustaining hamstring strain injuries. However, its efficacy is not supported by the current evidence. Current methods for the calculation of the H : Q ratio provide only a one- or two-dimensional ratio, often ignoring fundamental muscle mechanical properties. Based on isokinetic torque measurements of the knee flexors and extensors (0–400° s−1) in 25 young, physically active males, we derived a model equation that creates a three-dimensional H : Q functional ratio profile. The model robustness was tested against a different number of input torque data (8, 11, 14 and 17 pairs of points) and small perturbation of the knee joint angle data (5°). The model was consistent and behaved well under all conditions apart from the eight pairs of points (R2 = 0.84−0.96; RMSE = 0.14−0.25; NRMSE = 0.12−0.27), and the H : Q functional ratio was successfully described even at angles and velocities that cannot be normally assessed with isokinetic dynamometry. Overall, our results suggest that the model can provide a fast and accurate three-dimensional description of the knee joint muscle strength balance using as few as 11 experimental data points and this could be an easy-to-employ screening tool.

Line 230-241. This paragraph is very difficult to follow and quite cryptic. Table 1 surely helps. Also why did not the authors also run on optimisation to find the set of points needed for the best fit?
Line 273-278. I do not believe this is a rigorous way to carry out a cross-validation.  Decision letter (RSOS-210696.R0) We hope you are keeping well at this difficult and unusual time. We continue to value your support of the journal in these challenging circumstances. If Royal Society Open Science can assist you at all, please don't hesitate to let us know at the email address below.

Dear Dr Voukelatos
The Editors assigned to your paper RSOS-210696 "A three-dimensional description of the Hamstrings:Quadriceps functional ratio" have now received comments from reviewers and would like you to revise the paper in accordance with the reviewer comments and any comments from the Editors. Please note this decision does not guarantee eventual acceptance.
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Kind regards, Royal Society Open Science Editorial Office I share similar concerns regarding the representation of the study approach and methodology. In particular, it was not clear from the outset that the study involves both a meta-analysis of previous data collected and published by the authors, as well as a new experimental data set. This can be clarified. Also, there is not very much information on the new experimental methodology. In fact, as far as I understood, there is more detailed information provided for the previously published experiment. For example, there is no information on the subject characteristics or the specific experimental procedures that were performed in the new experiments. Also, if studies were performed on human subjects, information on human ethics approval should be documented.

Minor points:
Lines 69-81. From this paragraph, it is not immediately clear how the study of Hiemstra et al that uses omega and theta is a 2D analysis but your study also using omega and theta is considered a 3D analysis.
Lines 131-156. There is a lot of detailed information provided on the methodology that has been previously published. This could be simplified, and more detail could instead be provided for the new experiments performed.
Line 438. "accurate enough" is subjective. Consider rewording. If the conclusion is that it is an accurate approach, it could simply be stated as such.
Besides the methodological concerns, I also feel that the study can provide a valuable new tool to help practitioners assess the H:Q ratio. As such, I hope that these concerns can be addressed in a revision.
Although the work done can be seen as slightly incremental, the authors have tried to improve the current body of literature by using a combination of datasets and newly collected data to validate their computational work.
As better explained here below, there are some major issues related to current version of the paper: 1. The methods sections should be restructured and written more plainly as at the moment it is very difficult to follow. For example the steps used to calculate the Re and Rt functions (and the final identification fo the best parameters of the plane curves) could be summarised and better explained using a figure.
2. The rationale for using a specific dataset for model implementation and then model validation should be discussed and clarified. The author should consider to pool all the data and randomly identify the training and validation datasets or even perform a cross-validation with all data. This is key to provide the best fit possible and better evaluate the model robustness. 3. The minimum number of points need to fit the curves should be identified using an optimisation. 4. The fit evaluation using different number of points generates rather different curves with predicted values for high angles and velocities that can vary dramatically. This can generate much bigger errors than the RMSE reported and also provide wrong prediction for hamstring injuries during high velocity tasks. This point should be addressed.
Line 46-57. Although this is a well written paragraph more info on the type of analysis used to predict hamstring injury using such metrics should be clarified. If those studies only featured correlation approaches, also the methods should be listed as a potential limitation.

METHODS
Personally, I would include the experimental methods fist and use subheadings to split them from the theoretical ones.
Line 91-122. This is a rather difficult paragraph to follow without reading any previous work, and the use of Re and Rt is a bit confusing. Perhaps a figure here to show the different steps and meaning of parameters would help.
The parameter optimised should be more clearly highlighted to avoid confusion with the ones inputted from experimental measurements.
Line 136 -Clarify how angular velocities were converted. At the moment the wording makes it unclear.
Line 205. I believe that a cross-validation approach should be embrace to evaluate the groupdependency. It is unclear if this was done only once.
Line 230-241. This paragraph is very difficult to follow and quite cryptic. Table 1 surely helps. Also why did not the authors also run on optimisation to find the set of points needed for the best fit?
Line 273-278. I do not believe this is a rigorous way to carry out a cross-validation.  Your revised paper should include the changes requested by the referees and Editors of your manuscript. You should provide two versions of this manuscript and both versions must be provided in an editable format: one version identifying all the changes that have been made (for instance, in coloured highlight, in bold text, or tracked changes); a 'clean' version of the new manuscript that incorporates the changes made, but does not highlight them. This version will be used for typesetting if your manuscript is accepted.
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Author's Response to Decision Letter for (RSOS-210696.R0) See Appendix A.

Do you have any ethical concerns with this paper? Yes
Have you any concerns about statistical analyses in this paper? No

Recommendation?
Accept with minor revision (please list in comments)

Comments to the Author(s)
The methods of the paper have been more clearly described. However the authors could put a bit more effort in making figure 1 more palatable (i.e. by adding respective graphs) and easier to understand.
The conclusion should clearly provide guidelines on the number of points (or experiments) that should be done to use the equation correctly. This does not come up clearly from the conclusion and should be included in the abstract too.
Also I feel that the title could be improve. The key message is to be able to use few experimental points as inputs to a novel equation to estimate H:Q ratio. The '3-D dimensional' description is not very helpful to me.

SPECIFIC COMMENTS
Line 98 -Please avoid the use of acronyms in this first sentence as it hinders the readability.  . How did the authors vary the combinations? What was the rationale for moving from linear to non-linear? I think this needs more explanation.
Line 199 Perhaps I am missing something but how can the authors test the best fit using the same 11 subject? Should not this be tested on the 14 subject database? Perhaps the authors are referring to testing the robustness of the 17 points?
Line 198-201. I am sorry but this paragraph is still too cryptic.

Decision letter (RSOS-210696.R1)
We hope you are keeping well at this difficult and unusual time. We continue to value your support of the journal in these challenging circumstances. If Royal Society Open Science can assist you at all, please don't hesitate to let us know at the email address below.

Dear Dr Voukelatos
On behalf of the Editors, we are pleased to inform you that your Manuscript RSOS-210696.R1 "A three-dimensional description of the Hamstrings:Quadriceps functional ratio" has been accepted for publication in Royal Society Open Science subject to minor revision in accordance with the referees' reports. Please find the referees' comments along with any feedback from the Editors below my signature.
We invite you to respond to the comments and revise your manuscript. Below the referees' and Editors' comments (where applicable) we provide additional requirements. Final acceptance of your manuscript is dependent on these requirements being met. We provide guidance below to help you prepare your revision.
Please submit your revised manuscript and required files (see below) no later than 7 days from today's (ie 09-Mar-2022) date. Note: the ScholarOne system will 'lock' if submission of the revision is attempted 7 or more days after the deadline. If you do not think you will be able to meet this deadline please contact the editorial office immediately.
Please note article processing charges apply to papers accepted for publication in Royal Society Open Science (https://royalsocietypublishing.org/rsos/charges). Charges will also apply to papers transferred to the journal from other Royal Society Publishing journals, as well as papers submitted as part of our collaboration with the Royal Society of Chemistry (https://royalsocietypublishing.org/rsos/chemistry). Fee waivers are available but must be requested when you submit your revision (https://royalsocietypublishing.org/rsos/waivers).
Thank you for submitting your manuscript to Royal Society Open Science and we look forward to receiving your revision. If you have any questions at all, please do not hesitate to get in touch. As you will see, the review is generally positive. However, R1 raises some concerns that should be addressed. In particular, the reviewer's suggestions for Figure 1 and their comments about the concluding remarks can help improve your manuscript. I hope that you find the reviewer comments helpful I look forward to seeing a revised manuscript.

Best Regards, Jonas Rubenson
Reviewer comments to Author: Reviewer: 1 Comments to the Author(s) The methods of the paper have been more clearly described. However the authors could put a bit more effort in making figure 1 more palatable (i.e. by adding respective graphs) and easier to understand.
The conclusion should clearly provide guidelines on the number of points (or experiments) that should be done to use the equation correctly. This does not come up clearly from the conclusion and should be included in the abstract too.
Also I feel that the title could be improve. The key message is to be able to use few experimental points as inputs to a novel equation to estimate H:Q ratio. The '3-D dimensional' description is not very helpful to me.

SPECIFIC COMMENTS
Line 98 -Please avoid the use of acronyms in this first sentence as it hinders the readability. You should provide two versions of this manuscript and both versions must be provided in an editable format: one version should clearly identify all the changes that have been made (for instance, in coloured highlight, in bold text, or tracked changes); a 'clean' version of the new manuscript that incorporates the changes made, but does not highlight them. This version will be used for typesetting.
Please ensure that any equations included in the paper are editable text and not embedded images.
Please ensure that you include an acknowledgements' section before your reference list/bibliography. This should acknowledge anyone who assisted with your work, but does not qualify as an author per the guidelines at https://royalsociety.org/journals/ethicspolicies/openness/.
While not essential, it will speed up the preparation of your manuscript proof if you format your references/bibliography in Vancouver style (please see https://royalsociety.org/journals/authors/author-guidelines/#formatting). You should include DOIs for as many of the references as possible.
If you have been asked to revise the written English in your submission as a condition of publication, you must do so, and you are expected to provide evidence that you have received language editing support. The journal would prefer that you use a professional language editing service and provide a certificate of editing, but a signed letter from a colleague who is a proficient user of English is acceptable. Note the journal has arranged a number of discounts for authors using professional language editing services (https://royalsociety.org/journals/authors/benefits/language-editing/).

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--If you have uploaded any electronic supplementary (ESM) files, please ensure you follow the guidance at https://royalsociety.org/journals/authors/author-guidelines/#supplementarymaterial to include a suitable title and informative caption. An example of appropriate titling and captioning may be found at https://figshare.com/articles/Table_S2_from_Is_there_a_trade-off_between_peak_performance_and_performance_breadth_across_temperatures_for_aerobic_sc ope_in_teleost_fishes_/3843624. At the 'Review & submit' step, you must view the PDF proof of the manuscript before you will be able to submit the revision. Note: if any parts of the electronic submission form have not been completed, these will be noted by red message boxes -you will need to resolve these errors before you can submit the revision. Decision letter (RSOS-210696.R2) We hope you are keeping well at this difficult and unusual time. We continue to value your support of the journal in these challenging circumstances. If Royal Society Open Science can assist you at all, please don't hesitate to let us know at the email address below.

Dear Dr Voukelatos,
It is a pleasure to accept your manuscript entitled "The Hamstrings:Quadriceps functional ratio expressed over the full angle-angular velocity range using a limited number of data points" in its current form for publication in Royal Society Open Science.
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Thank you for your fine contribution. On behalf of the Editors of Royal Society Open Science, we look forward to your continued contributions to the Journal. Comments to the Author: Dear Dr. Voukelatos and co-authors, As you will see, the review is overall positive. Nevertheless, it raises some concerns that you will need to address before this work can be considered for publication. Specifically, Reviewer 1 raises important concerns regarding the description of the methodology that needs to be addressed.
I share similar concerns regarding the representation of the study approach and methodology. In particular, it was not clear from the outset that the study involves both a meta-analysis of previous data collected and published by the authors, as well as a new experimental data set. This can be clarified. Also, there is not very much information on the new experimental methodology. In fact, as far as I understood, there is more detailed information provided for the previously published experiment. For example, there is no information on the subject characteristics or the specific experimental procedures that were performed in the new experiments. Also, if studies were performed on human subjects, information on human ethics approval should be documented.